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\pard\li180\cf2\ulnone\caps0\fs24 Maximum Likelihood Hebbian Learning\cf3\par
\cf0\b0\par
\pard\li180\ri1484\qj\tx7020\fs18 En este apartado presentamos una extensi\'f3n de las reglas de aprendizaje de Redes de An\'e1lisis de Componentes Principales (PCA), las cuales han sido derivadas para ser \'f3ptimas para una funci\'f3n de densidad de probabilidad espec\'edfica.  Esta familia completa de reglas de aprendizaje son m\'e9todos de desarrollo de B\'fasqueda Exploratoria de Proyecciones.\par
\par
Varias investigaciones han demostrado que las reglas de aprendizaje pueden derivar aproximadamente en una mejor l\'ednea de comprensi\'f3n de los datos. Entonces podemos comenzar con la funci\'f3n de coste:\par
\fs24\par
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}}}\f0\fs24\par
\pard\li180\ri1484\qc\tx7020\par
\pard\li180\ri1484\qj\tx7020\fs18 La cual vamos a minimizar para conseguir la actualizaci\'f3n de los pesos seg\'fan la regla de Hebb.\par
\par
La minimizaci\'f3n de J es equivalente al logaritmo negativo de la probabilidad del residuo, e, si e es la Gaussiana y es igual a maximizar la probabilidad del residuo.\par
Permite al residuo tener una funci\'f3n de densidad de probabilidad:\par
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}}}\f0\fs24\par
\par
\pard\li180\ri1484\qj\tx7020\fs18 Luego denotamos una funci\'f3n de coste general asociada a la red como:\par
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}}}\cf3\b\f0\fs24\par
\pard\li180\ri1484\qj\tx7020\cf0\b0\fs18 donde k es una constante. Realizando gradiente descendente en J se obtiene:\par
\pard\li180\ri1484\tx7020\f1\fs20{\object\objemb{\*\objclass Equation.3}\objw4220\objh620{\*\objdata 
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}}}\cf3\b\f0\fs24\par
\pard\li180\ri1484\qj\tx7020\cf0\b0\fs18 donde T es la traspuesta del vector. \par
\par
Se debe esperar que para residuos leptoc\'farticos (con mayor curtosis que una distribuci\'f3n Gaussiana), valores de p<2 deber\'edan ser apropiados, mientras que para residuos mesoc\'farticos (menor curtosis que la Gaussiana), valores de p>2 ser\'e1n los apropiados. Es com\'fan creer que es menos importante obtener exactamente la distribuci\'f3n correcta cuando se busca para una fuente espec\'edfica, que obtener una distribuci\'f3n correcta aproximada, es decir todas las se\'f1ales supergausianas pueden conseguirse utilizando una distribuci\'f3n gen\'e9rica leptoc\'fartica, y todas las se\'f1ales subgausianas pueden conseguirse  utilizando una distribuci\'f3n gen\'e9rica mesoc\'fartica.\par
\pard\li180\ri1484\tx7020\cf3\b\fs24\par
\pard\li180\ri1484\qj\tx7020\cf0\b0\fs18 Los experimentos realizados tienden a soportar esta creencia para alguna proporci\'f3n, pero a menudo se obtiene precisi\'f3n y es mejor la velocidad de convergencia cuando se consigue mayor precisi\'f3n en la elecci\'f3n de p.\par
\par
Luego vemos como son las operaciones de la red:\par
\pard\li180\ri1484\tx7020\cf3\b\fs24\par
\pard\li180\ri1484\qj\tx7020\cf0\b0\fs18 Feedforward o alimentaci\'f3n hacia delante:\par
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\pard\li180\ri1484\qj\tx7020\cf0\b0\fs18 Actualizaci\'f3n de pesos:\par
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}}}\cf3\b\f0\fs24\par
\par
\pard\li180\ri1484\qj\tx7020\cf0\b0\fs18 (Fyfe y McDonald, 2001) usan un solo valor de p (p=1) en esta regla  y describen este m\'e9todo realizando un tipo de PCA, pero esto no es estrictamente cierto ya que s\'f3lo la regla Hebbiana original realiza PCA. Puede parecer m\'e1s apropiado unir esta familia de reglas de aprendizaje al An\'e1lisis de Factores Principales, ya que este m\'e9todo hace una suposici\'f3n sobre el ruido en un conjunto de datos y luego elimina el ruido de la estructura de covarianza de los datos, antes de realizar PCA. Se hace algo similar aqu\'ed, ya que se basa en la regla tipo PCA en la distribuci\'f3n supuesta del residuo. Maximizando la probabilidad del residuo con respecto a la distribuci\'f3n actual, se est\'e1 asociando la regla de aprendizaje al pdf del residuo.\par
\pard\li180\ri1484\tx7020\cf3\b\fs24\par
\pard\li180\ri1484\qj\tx7020\cf0\b0\fs18 M\'e1s importante es enlazar este m\'e9todo al m\'e9todo est\'e1ndar estad\'edstico de EPP: ahora la naturaleza y cuantificaci\'f3n de lo interesante es en t\'e9rminos de c\'f3mo probables son los residuos bajo un modelo particular de pdf de los residuos. Tambi\'e9n se \ldblquote blanquean\rdblquote  los datos antes de aplicar el m\'e9todo de aprendizaje y con este m\'e9todo tambi\'e9n se encuentran estructuras interesantes en los datos.\par
\pard\li180\ri1484\tx7020\cf3\b\fs24\par
\par
\pard\cf0\b0\f1\fs20\par
}
 